The SK has 14 potential targets, each equally likely. The Escort has 14 potential targets, each equally likely. So there is a 1/14 chance the Escort RBed the SK and a 1/14 chance the SK targeted the Escort. If they both target each other (1/196 chance), that person is still the SK. So there's a 1/14 chance the Escort targets the SK and a (1/14 - 1/196) chance the SK targeted the Escort without being the Escort's target.

From there we get:

(1/14) / (1/14 + 1/14 - 1/196) = ~52% chance the Escort's target is the SK if the Escort died to the SK.

It's actually pretty straightforward if I spell out everything I left implicit.

First, there's the probability of the Escort targeting the SK. There are 14 targets they can choose and only 1 of them is the SK so that means 1/14 chance of choosing the SK.

Second, there's the probability of the SK targeting the Escort. There are 14 targets they can choose and only 1 of them is the Escort so that means 1/14 chance of choosing the Escort.

Third, there's the probability of them targeting each other. Since they are choosing independently without influencing each other we can just multiply the probability that the Escort chooses the SK by the probability the SK chooses the Escort. This gives us 1/14 * 1/14 = 1/196.

From here, it's a matter of determining what happens in each of the scenarios. The 1/14 times the Escort targets the SK, whoever they visited will be SK. The 1/14 times the SK targets the Escort, whoever the Escort visited will not be SK except for the 1/196 times that the Escort also targets the SK. Slightly rewording, this means that (1/14 - 1/196) times, the SK will kill Escort without the Escort visiting the SK. We can add the 1/14 for the Escort targeting the SK and the (1/14 - 1/196) for the SK targeting the Escort to get (1/14) + (1/14 - 1/196) chance of the SK killing the Escort.

Putting this all together, we just need to take the ratio of times the Escort targets the SK (1/14) to times that the Escort dies to SK at all to get (1/14) / (1/14 + 1/14 - 1/196). And that's a hair under 52%.

If you're the dead Escort, the SK, or the person RBed then you obviously know with certainty whether the RBed person is SK. Other than that, no, I don't believe the probability is affected by your own role in this scenario.

It's not almost guaranteed but it is a high enough probability to be the one of the best leads you can get so early. I don't know how many people know the actual probability but I know that I often exaggerate the probability in that scenario just to get town to listen. Especially if I'm SK and killed an Escort who targeted someone else :)

so it's almost unaffected by the number of players alive, interesting.

This shouldn't be too surprising, right? Assuming 1 Escort, 1 SK, and uniformly random targets, there's an equal probability that the Escort targets the SK as there is that the SK targets the Escort. The only thing that bumps the probability above 50% is the case where they target each other, which becomes more likely as population gets smaller. Also note that the graph asymptotically approaches 1/2 for large populations.

However, the main reason for focusing on N1--besides being a relatively known state--is that the probability is massively affected by the rest of the game. For example, if somebody announces "I RBed so-and-so last night", the SK might want to target them both to remove a means of finding the SK and to get somebody else lynched as well.

Assuming both people visit someone the first night, there are 196 permutations of who those 2 people visit. Of those 196, there are 27 permutations in which Escort dies to SK the first night, as the other 169 have both people not visiting each other.

Escort visits SK, SK visits anyone else (counts as 13 permutations, as SK can visit anyone else in town, and it will still happen)

SK visits Escort, Escort visits anyone else (counts as 13 permutations, as Escort can visit anyone else in town, and it will still happen)

SK and Escort both visit the other person (counts as 1 permutation)

Of those 27, Escort visits SK in 14 of them.

Because of this, there is a 14 in 27, or about a 51.85% chance that Escort visited SK.

I'll forego the math since I suck at it and just say this: always read the death notes. If there is a message in there that was obviously meant for a different player than the one who died, you have your answer.